Online research in philosophy

Marr's computational theory of stereopsis is shown to imply that human vision employs a system of representation which has all the properties of a number system. Claims for an internal number system and for neural computation should be taken literally. I show how these ideas withstand various skeptical attacks, and analyze the requirements for describing neural operations as computations. Neural encoding of numerals is shown to be distinct from our ability to measure visual physiology. The constructs in Marr's theory are neither propositional nor pictorial, and provide a counter example to many commonly held dichotomies concerning mental representation.

I argue that neural activity, strictly speaking, is not computation. This is because computation, strictly speaking, is the processing of strings of symbols, and neuroscience shows that there are no neural strings of symbols. This has two consequences. On the one hand, the following widely held consequences of computationalism must either be abandoned or supported on grounds independent of computationalism: (i) that in principle we can capture what is functionally relevant to neural processes in terms of some formalism taken from computability theory (such as Turing Machines), (ii) that it is possible to design computer programs that are functionally equivalent to neural processes in the same sense in which it is possible to design computer programs that are functionally equivalent to each other, (iii) that the study of neural (or mental) computation is independent of the study of neural implementation, (iv) that the Church-Turing thesis applies to neural activity in the sense in which it applies to digital computers. On the other hand, we need to gradually reinterpret or replace computational theories in psychology in terms of theoretical constructs that can be realized by known neural processes, such as the spike trains of neuronal ensembles.Â.

It has been argued that neural networks and other forms of analog computation may transcend the limits of Turing-machine computation; proofs have been offered on both sides, subject to differing assumptions. In this article I argue that the important comparisons between the two models of computation are not so much mathematical as epistemological. The Turing-machine model makes assumptions about information representation and processing that are badly matched to the realities of natural computation (information representation and processing in or inspired by natural systems). This points to the need for new models of computation addressing issues orthogonal to those that have occupied the traditional theory of computation.

I argue that neural activity, strictly speaking, is not computation. This is because computation, strictly speaking, is the processing of strings of symbols, and neuroscience shows that there are no neural strings of symbols. This has two consequences. On the one hand, the following widely held consequences of computationalism must either be abandoned or supported on grounds independent of computationalism: (i) that in principle we can capture what is functionally relevant to neural processes in terms of some formalism taken from computability theory (such as Turing Machines), (ii) that it is possible to design computer programs that are functionally equivalent to neural processes in the same sense in which it is possible to design computer programs that are functionally equivalent to each other, (iii) that the study of neural (or mental) computation is independent of the study of neural implementation, (iv) that the Church-Turing thesis applies to neural activity in the sense in which it applies to digital computers. On the other hand, we need to gradually reinterpret or replace computational theories in psychology in terms of theoretical constructs that can be realized by known neural processes, such as the spike trains of neuronal ensembles.

If connectionism is to be an adequate theory of mind, we must have a theory of representation for neural networks that allows for individual differences in weighting and architecture while preserving sameness, or at least similarity, of content. In this paper we propose a procedure for measuring sameness of content of neural representations. We argue that the correct way to compare neural representations is through analysis of the distances between neural activations, and we present a method for doing so. We then use the technique to demonstrate empirically that different artificial neural networks trained by backpropagation on the same categorization task, even with different representational encodings of the input patterns and different numbers of hidden units, reach states in which representations at the hidden units are similar. We discuss how this work provides a rebuttal to Fodor and Lepore's critique of Paul Churchland's state space semantics.

Biological neural computation relies a great deal on architecture, which constrains the types of content that can be processed by distinct modules in the brain. Though artificial neural networks are useful tools and give insight, they cannot be relied upon yet to give definitive answers to problems in cognition. Knowledge re-use may be driven more by architectural inheritance than by epistemological drives.

I address whether neural networks perform computations in the sense of computability theory and computer science. I explicate and defend
the following theses. (1) Many neural networks compute—they perform computations. (2) Some neural networks compute in a classical way.
Ordinary digital computers, which are very large networks of logic gates, belong in this class of neural networks. (3) Other neural networks
compute in a non-classical way. (4) Yet other neural networks do not perform computations. Brains may well fall into this last class.